1/(123)+1/(234)+1/(345)+1/(456)+.+1/(242526)=?

来源：学生作业帮助网编辑：作业帮时间：2024/11/08 20:53:35

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(24*25*26)=?
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(24*25*26)=?

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(24*25*26)=?
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(24*25*26)
=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+……+1/2*(1/24*25-1/25*26)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/24*25-1/25*26)
=1/2*(1/1*2-1/25*26)
=1/2*(1/2-1/650)
=81/325

用逐差法~~~！
原式=(1-1/2-1/3)+(1/2-1/3-1/4)+……+(1/24-1/25-1/26)=
算出结果就好啦~很多项都约去了很容易算出结果我就不帮你算啦~

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